Which of the following numbers is a factor of 88? ${3,6,9,10,11}$
Explanation: By definition, a factor of a number will divide evenly into that number. We can start by dividing $88$ by each of our answer choices. $88 \div 3 = 29\text{ R }1$ $88 \div 6 = 14\text{ R }4$ $88 \div 9 = 9\text{ R }7$ $88 \div 10 = 8\text{ R }8$ $88 \div 11 = 8$ The only answer choice that divides into $88$ with no remainder is $11$ $ 8$ $11$ $88$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $11$ are contained within the prime factors of $88$ $88 = 2\times2\times2\times11 11 = 11$ Therefore the only factor of $88$ out of our choices is $11$. We can say that $88$ is divisible by $11$.